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\begin{document}
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\title{Transmitter Power Aware in mm-Wave\\ mesh-topology based WiNoC} 

\author{\IEEEauthorblockN{Andrea Mineo}
\IEEEauthorblockA{University of Catania, Italy\\
amineo@dieei.unict.it}
\and
\IEEEauthorblockN{Maurizio Palesi}
\IEEEauthorblockA{Kore University, Italy\\
maurizio.palesi@unikore.it}
\and
\IEEEauthorblockN{Giuseppe Ascia\\ and Vincenzo Catania}
\IEEEauthorblockA{University of Catania, Italy\\
\{gascia,vcatania\}@dieei.unict.it}}
\maketitle

%------------------------------------------------------------------------------
\begin{abstract}
Recently, in the context of the Network-on-Chip, many emergents technique has been
proposed for alleviate the problem of latency and power consumption presents
when the number of core increase. A viable proposed solution is called WiNoC
in which the traditional wired link are substituting  with the use of
wireless medium. Unfortunately the power dissipated by the introduced RF transceiver 
and in particular of the transmitter, constitutes the dominant fraction of the 
overall communication infrastructure. For this reason, in this paper 
we propose a new technique and methodology for reducing the power consumption of the
transmitter, modulating the required transmitting power with the knowledge
of the estimated attenuations introduced by the wireless medium after an 
accurate modelling and analysis with an commercial 3D field solver.
\end{abstract}
%------------------------------------------------------------------------------
\section{Introduction}
\label{sec:intro}

In the last few years we had assist the transition from single-core to many-core era. 
Some microprocessor foundries such as AMD, Intel and TILERA have yet released many 
commercial product that use multi-core technology. In particular, AMD in this last year 
has released the first native eight core  processor fabricated in 32-nm~\cite{amd_eight} 
for the desktop market, while TILERA have yet released a first commercial 72 core SoC 
operating at 1.2GHz~\cite{tilera_72}. On the research side, Intel has demonstrated his 
capability of integrate 80 core~\cite{vangal_jssc08} in a single package, and more recently 
has integrated 45 P54C Pentium core in a single chip called SCC~\cite{intel_scc} that 
use Network on chip as interconnect paradigm. Network-on-Chip (NoC) is a viable solution 
for tackling the interconnect bottleneck, substituting a single shared medium with an 
packets switched based network~\cite{dally_dac01}. 
One of the mayor design challenge of a NoC is minimize the introduced overhead in therms 
of Area, energy consumption and latency. In Particular, for mesh-based NoC this last therm 
become a problem when the number of core increase. 
For this reason, many emergents solution such as 3D-stacked NoC, optical and radio frequency 
based solution has been proposed. In particular,  this last solution can be divided in two 
main families called RF-I~\cite{chang_hpca08} and Wireless NoC respectively~\cite{zhao_tc08}. 
The first one is based on the propagation at the speed of light (effective) of an electromagnetic
wave through an waveguide constituted by two close conductor  using standard CMOS technology. 
This waveguide acts as an highway for the travelling information. 
The RF-I solution has demonstrated his effectiveness in therms of latency and power~\cite{chang_micro08} 
but his performance don't scale fine when the numbers of core increase. The other solution, 
called Wireless NoC (WiNoC), has been proposed for resolving the scalability problem introducing an wireless 
backbone upon the traditional wire-based NoC~\cite{deb_jetcas12}.
Several works was born with this emergents technology defining several architectures. 
In particular in ~\cite{deb_jetcas12} the authors divided this architectures in two main family 
called mesh-topology based and small-world based~\cite{ogras_tvlsi06} WiNoC. The first ones uses a regular 
clustered 2D-mesh topology in which are situated the RF switches and antennas, while the second one 
use the concept of small world that defines two hierarchical layers. The top level can be 
interconnect by wired or wireless medium, while the bottom layers subnets can be interconnected 
using only the traditional wired link. With this structure, every subnet and the top layer can 
be have an their customized topology such as mesh, ring etc.. \\The wireless NoC infrastructure, 
introduces new hardware resource that constituted an overhead in therms of area and power 
consumption. In particular, the major contribution of power is related to the radio 
transmitter front-end connected to the antenna. All cited works estimate the 
worst case power required for transmitting the data under an reliability constrain such as
the bit error rate (BER), and transmit at this power level using the ASK-OOK modulation.
For example in~\cite{yu_mwscas11} the transmitter is responsible for about 65$\%$ of the
overall transceiver power consumption, while in~\cite{daly_jssc07} this contribute can be
of 74,4$\%$.
\\ 
As we will see in the Sec.\ref{sec:background} the required transmitting power depending by several 
factor which not can be  easily predicted with an pen and paper analysis, but requires an accurate 
3D field solver modelling and analysis. For this reason, in this work we proposed an accurate 
and systematic analysis of the power needed at the transmitter using HFSS~\cite{hfss} as field solver 
and by placing a couple of antennas in several fixed point of the silicon die estimating the 
power attenuation (Ga) introduced by the wireless medium for each communications using the Friis formula. 
Finally, with this information we can modulate the transmitting power only  with the information about 
the position of the transmitter an receivers radio hub and by the relative attenuation.\\
The experiments conduits with the our scheme applied at the state of art architectures presents 
in literature shown a power saving up to 50.2 \% with the introduction of a negligible hardware overhead 
(only 80 $\mathrm{\mu m^2}$ for each transceiver). \\
The rest of the papers is organized as follow. Section~\ref{sec:related} describes  the related work 
in the context of intra chip communication with an particular emphasis introducing the mesh-topology
based wireless Network-on-Chip (WiNoC). The background for determinate the signal strength requirements
for OOK modulation are described in Section~\ref{sec:background}. In the same section the Friis
transmission equation have been described for estimate the level of attenuation introduced
by the wireless medium. In Section~\ref{sec:proposed} the proposed work is explained
with the introduction of various design rules for build an power aware, energy efficient
mesh-topology based WiNoC. Finally, before the conclusions, the experimental results for various 
specific case are showed in the Section~\ref{sec:experimental}.
%------------------------------------------------------------------------------
\section{Related works}
  \label{sec:related}
\subsection{Wireless interconnect with integrated antennas}

The possibility of radio communications inside the chip is a novel technique born 
initially for distributing clock signals inside the chip reducing the problem of the 
clock skew\cite{floyd_jssc02}. The main drawback until then, was the capability of 
integrate an antenna in a standard silicon substrate compatibly with the CMOS 
technology. This is linked by the capability of the transistors of operate at high 
frequency(see Tab.\ref{tab:itrs}). This is because for propagate a signal, the antenna's 
dimension can be usually comparable with the wavelength. For example, at 60 GHz an dipole 
antenna, constituted simply by two conductor, must have a length of $\mathrm{632\times2 \ \mu m}$ 
when integrated in a silicon substrate~\cite{gutierez_jsac09}, while if operating 
in 5.8 GHz should be a dimension of $\mathrm{6.5\times2 \ mm}$ , then comparable with 
the entire size of die. Fortunately, the dimensions scaling do not occurs only in the 
antenna but also in the passive devices inside the main building blocks of the RF front 
end, which consumes a dominant portion of area. For example, if we consider an simple amplifier 
which operate at high frequency such as the common emitter in Fig.~\ref{fig:rf_amplifier}, 
we should usually sizing the $CL$ group in order to resonate at the centre of the 
operating band. Consequently, let consider the sum of the admittance expressed as follow:

\begin{equation}
  Y_p=Y_C+Y_L=j \omega_c C+ \frac{1}{j\omega_c L}=j\bigg(\omega_c C-\frac{1}{\omega_c L}\bigg)
  \label{eq:ammettance}
\end{equation} 

usually one of the design step is set the admittance to zero at the target frequency 
(centre of band) therefore if the C is the parasitics capacitance which depends by the 
active devices and by the other effect such as the contact capacitance and the parasitics 
capacitance introduced by the inductor itself and $\omega_C$ is the operating frequency, 
we should set the inductor's value by:

\begin{equation}
  L=\frac{1}{\omega^2_c C}
  \label{eq:set_ammettance}
\end{equation} 

This means that at higher frequency the value of the inductance can be setted lower.
In fact, as reported in~\cite{chang_hpca08}, at 20 GHz the size of inductor is approximately
$\mathrm{50\mu m\times 50 \mu m}$ while at 400 GHz can be small as $\mathrm{12\ \mu m\times 12 
\ \mu m}$.\\ This just mentioned consideration lead various research group to try the integration 
of every building block of RF front end, comprised the antenna, inside the same SoC.  Therefore,
many research works has been develop such as in~\cite{floyd_jssc02,o_ted05,lin_jssc07}.

\begin{figure}
  \centering
  \includegraphics[width=0.35\textwidth ,angle=270]{pictures/lna.eps}
  \caption{Generic Common Source RF amplifier.}
  \label{fig:rf_amplifier}
\end{figure}

\begin{table}
  \centering
  \caption{ITRS projections for the transition frequency $f_t$ and maximum 
  oscillating frequency $f_{max}$\cite{itrs_rfams12}.}
  \label{tab:itrs}
  \begin{tabular}{lcccccc}
    \hline
    Year 				& 2012 	& 2013 & 2014 & 2015 & 2016 & 2017 	\\
    \hline
    $ f_t $(GHz) 		& 315 	& 315  & 345  & 360  & 375  & 390 	\\
    $ f_{max}$(GHz) 	& 420   & 455  & 490  & 525  & 560  & 595  	\\
    \hline
  \end{tabular}
\end{table}
%------------------------------------------------------------------------------
\subsection{Mesh-Topology Based WiNoCs}

The considerations just made, lead various NoC's research group to try
the insertion of long range wireless link upon the traditionally wire-based
Network-on-Chip. A exhaustive panoramic of the state of art can be found in
~\cite{deb_jetcas12} in which the authors dividing the various Wireless
architecture in two main families called mesh-topology based and small-topology 
world based WiNoCs. Another classification can be done on the basis of 
the portion of electromagnetic spectrum used for transmit the data
such as UWB~\cite{zhao_tc08} (few GHz), mm-wave~\cite{deb_asap10,ditommaso_hoti11
,deb_isqed12,deb_glsvlsi12} (tens of GHz), 
sub-THz~\cite{lee_mobicom_09} (hundreds of GHz) and THz~\cite{ganguly_tc10} NoC.
In particular, this last one uses carbon nanotubes as antenna, while 
the others uses the metallization present in standard CMOS technology as antenna.
In particular, in all work  that use mm-wave, the zigzag antenna Fig.\ref{fig:zigzag} was
proposed as the best candidate. In our work we prefer this last kind of antenna 
because his behaviour can be more easily predict with yet consolidate technique 
and knowledge such as an systematic use of field solver for modelling and analysis.
Furthermore, the use of regular structure such as the mesh topology based NoCs
are preferred because some symmetries can be useful used for simplify the design
and characterization of their physical structure.
Many example of mesh-topology based that use wireless link can be found 
in~\cite{lee_mobicom_09,ditommaso_hoti11,zhao_nocs11,wang_pdp11}.\\
For adapt the baseband signal to the wireless medium the most used
modulation are ASK-OOK (Amplitude Shift Keying or On Off Keying)
because require simply modulation and demodulation circuitry which impact
directly in the transceiver's complexity. Many example of transceiver 
that implement this kind of modulation can be found described in \cite{deb_asap10,
ditommaso_hoti11,deb_jetcas12}. On the other hand , the ASK-OOK
require too much transmitter power for met the reliability requirements
and have a poor spectral efficiency respect at more complex kind of modulation
such as the QAM (Quadrature Amplitude Modulation).

\begin{figure}
  \centering
  \includegraphics[width=0.4\textwidth]{pictures/zig_zag.eps}
  \caption{The zigzag antenna.}
  \label{fig:zigzag}
\end{figure}
%------------------------------------------------------------------------------
\section{Background}
  \label{sec:background}
\subsection{Friis transmission equation}
  \label{ssec:friis}
  
The required power output on the transmitter depends by many factor, such as the 
kind of modulation, the transceiver noise figure and by the attenuation introduced 
by wireless medium. In particular, referring at the Fig.\ref{fig:friis} which 
considers an transmitting antenna with an output power $P_t$ and an receiving 
antenna located at distance R with an relative angle respect their principal axis 
of $\theta_t,\phi_t$ for the transmitter antenna and $\theta_r,\phi_r$  for the 
receiver one, we can computed the portion of the transmitter power that reaches the 
terminal of the receiver antenna $P_r$ with the well known Friis transmission 
equation~\cite{balanis2008modern} valid when $R>2D^2/\lambda$, where D is the 
the maximum dimension of antenna (axial length for our case) and $\lambda$ is
the wavelength. The Friis equation is:

\begin{equation}
  G_a=\frac{P_r}{P_t}=e_t e_r \frac{\lambda^2 D_t(\theta_t,\phi_t)D_e(\theta_r,\phi_r)}
  {(4\pi R)^2}
  \label{eq:friis_simple}
\end{equation} 

where 
\begin{itemize}

  \item $e_t$ and $e_r$ are the efficiency of the transmitting and receiving antenna 
  respectively. This parameters represents the losses due usually by the non PEC 
  (Perfect Electrical Conductor) structure and in our cases mainly due to the silicon 
  substrate losses. For reduce this contribution high resistivity ($\mathrm{> 1 K\Omega.cm}$)  
  SOI (Silicon On Insulator) substrates can be used~\cite{montusclat_ecwt05} or an Polymide 
  stratus (few micron thick) can be inserted under the antenna~\cite{lee_mobicom_09}.
  
  \item  $D_t$ and $D_r$ are the directivity of the transmitting and receiving antenna
  respectively. This two functions quantity how much better the antenna can transmit or 
  receive in an specific direction.
  
  \item $\lambda$ is the effective wavelength. For an IC substrate  is estimated using 
  the material properties of the top IC layers (silicon dioxide $\epsilon_r=3.9$)~\cite{
  gutierez_jsac09}
  
\end{itemize}

The Eq.~\ref{eq:friis_simple} is valid starting form the assumption that both impedance of 
antenna are perfectly matched with the transceiver at the operating frequency and 
the polarization status of the transmitting and receiving antenna match also perfectly. 
This is an ideal situation, then for an accurate analysis we can consider the following 
formula: 

\begin{equation}
  G_a=\frac{P_r}{P_t}=e_t e_r \frac{\lambda^2 D_t(\theta_t,\phi_t)D_e(\theta_r,\phi_r)}{(4\pi R)^2} 
  \cdot(1-|\Gamma_t|)(1-|\Gamma_r|)|\hat{\rho_t}\cdot \hat{\rho_r}|
  \label{eq:friis_complex}
\end{equation} 

In that formula the $|\Gamma|$ therms refers to the portion of the transmitter or 
receiver power that return at the transmitter or at the antenna due to impedance
mismatch. This parameter known as reflection coefficient must be take in account 
don't only because affect the losses but mainly because this can causes an consistent 
temperature increase at the power devices attached at the antenna (transmitter side) 
which damage the RF front-end. Another therms introduced in that equation is the scalar 
product $|\hat{\rho_t}\cdot \hat{\rho_r}|$ (ideally equal to one) which can take in 
account the polarization status.\\ 
Unfortunately the knowledge of this parameter is impermissible wit a pen and paper 
study, then we can use the following formula useful for the estimation from measurements
via network analyser for realized prototypes or with field solver simulation~\cite
{floyd_jssc02}:

\begin{equation}
  G_a=\frac{P_r}{P_t}=\frac{|S_{12}|}{(1-|S_{11}|)(1-|S_{22}|)}
  \label{eq:friis_measured}
\end{equation} 

This formula give the information of the attenuation comprising the near-field 
contribute ($R<2D^2/\lambda$), because come from the information effectively 
measured at the antenna's terminals. 

\begin{figure}
  \centering
  \includegraphics[width=0.45\textwidth]{pictures/friis.eps}
  \caption{Friis transmission equation: reciprocal antennas positions.}
  \label{fig:friis}
\end{figure}
%------------------------------------------------------------------------------
\subsection{Power strength requirements}

The information obtainable from the Eq.~\ref{eq:friis_measured}, we have
the knowledge of the attenuation due to the wireless medium.
Since the reliability of the OOK is related to the energy spent per bit 
$E_b$ that reach the receiver's antenna terminal, we can determinate the 
power required on the transmitter side for each value of attenuation (Ga).
In particular for the OOK the BER (bit error rate) is given by:

\begin{equation}
  BER=Q\bigg( \sqrt{\frac{E_b}{N_0}}\bigg)
  \label{eq:ber}
\end{equation}
where the  $N_0$ is the transceiver noise spectral density and the 
Q function is the tail probability of the standard normal distribution 
which is defined as in Eq.~\ref{eq:q_func}.

\begin{equation} 
	\label{eq:q_func}
	Q(x)=\frac{1}{\sqrt{2\pi}}\int_{x}^{\infty} e^{-\frac{y^2}{2}}dy	 
\end{equation}

Since $E_b=P_r/R_b$ where $P_r$ is the power received at the terminal of the 
receiver antenna while $R_b$ is the data-rate, we can compute the required 
transmitter power for a given data-rate and BER requirements and for certain 
transceiver's thermal noise as:

\begin{equation}
  P_r=E_b \cdot R_b=(Q^{-1}(BER))^2N_0 \cdot  R_b
  \label{eq:pr}
\end{equation}

where $Q^{-1}$ is the inverse of the Q function.\\
In Fig.~\ref{fig:ber} is shown the BER at different level of received power 
(expressed in dBm\footnote{The absolute power can be expressed in dBm following 
the formula: \\$P_{dBm}=10\cdot Log(P_{lin}\cdot 10^3)$}). Considering the 
information obtained with the Eq.~\ref{eq:friis_measured}, we can finally compute 
the output power for each communications couple at the transmitter side as:

\begin{equation}
  P_t(dBm)=P_r(dBm)-G_a(dB)
  \label{eq:pt}
\end{equation}

where $P_r(dBm)$ can be calculated by hand using previous formulas while 
$G_a(dB)$ will be calculated using a field solver with the Friis formula.

\begin{figure}
  \centering
  \includegraphics[width=0.35\textwidth]{pictures/ber.eps}
  \caption{BER for different levels of received power.}
  \label{fig:ber}
\end{figure}
%------------------------------------------------------------------------------
\section{Proposed work}
\label{sec:proposed}

\subsection{Variable Gain Controller}
As mentioned in the introduction, under an reliability constrain, the 
designer must choose the correct level of transmitting power for each 
sources and destinations couple. This, not only impact on the power amplifier (PA) 
power consumption, but is more useful for attenuate the inter-channel interference 
when communications use different frequency (FDM). Therefore, this impact directly 
in a better communication's reliability.
This can be done after the introduction of an possible transceiver with 
the capability of power tuning. This is accomplished with the use 
of those type of power amplifier in which the output power can be digitally
adjustable such as in~\cite{daly_jssc07}. In the context or radiocommunications
such as mobile phone,wireless sensors network etc., this is yet an established 
technique but require more sophisticated controller's politics.\\
For the our purpose, aided by the regularity of the mesh-topology, we can propose 
an simple scheme for tune, at runtime, the power delivered to the antenna for each 
couple of communication under the reliability constrain discussed in the previous 
section. In Fig.~\ref{fig:tx_scheme} we shown the proposed transceiver in 
which the power is controlled by an specific block called \emph{VGA Controller}
(vga stand for variable gain amplifier) which output is attached directly to the 
power amplifier controllable circuitry. 
The proposed controller is enabled by the packet's header flit when this reach 
the radio hub. This kind of flit contains the information about the hub's  
destination address and then from this information and by the knowledge of the 
our position the \emph{VGA Controller} can drive the PA through $m$ bit in which $m$ 
depends by the number of digitally adjustable power step. In Fig.~\ref{fig:tx_scheme}
the block Ga represents the attenuation introduced by the wireless medium.
%------------------------------------------------------------------------------
\subsection{Power map determination}
\label{ssec:pmap_det}

After the introduction of enabling circuitry solution that can support
the proposed idea, we can trace the required  step for design an 
power aware wireless NoC.

\begin{enumerate}
  \item Clustering e placing: after the choice of the number of antenna presents
  on the NoC, which depends on the number of IP's and by the level of associativity $k$, 
  place the antennas in the proper position. In Fig.~\ref{fig:iwise} we divided the 
  die in 16 cluster. Each cluster contain an zigzag antenna at his centre.
  If we consider an $8\times8$ NoC, the level of associativity will be $k=4$.
  
  \item Attenuation's map determination: Draw the 3D model of the situation described 
  in the previous step and extract the scattering parameter $S_{11}, S_{22}$ using a 
  field solver such as HFSS. With this parameter apply the relation in the 
  Friis formula (Eq.~\ref{eq:friis_measured}). 
  This situation should be skip fabricating a test chip and measure the same parameter 
  with an network analyser (more accurate). In such test-chip the presents of power 
  grid and of others metal structure can be contemplated such as made in~\cite{o_ted05}.
  
  \item Power's map determination: after the choice of the transmission data-rate 
  and the required reliability constrain we can apply the Eq.~\ref{eq:pr} and the 
  Eq.~\ref{eq:pt}.

  \item Vga controller design: considering the number of available step, describing at
  RTL level an LUT (Look Up Table) with the information obtained by the previous step.
  Obviously this last value must be quantized considering ever the upper nearest 
  level of available power.
\end{enumerate}

\begin{figure}
  \centering
  \includegraphics[width=0.45\textwidth]{pictures/iwise.eps}
  \caption{A $16\times16$ cluster mesh based WiNoC.}
  \label{fig:iwise}
\end{figure}

\begin{figure}
  \centering
  \includegraphics[width=0.45\textwidth]{pictures/blocks.eps}
  \caption{Transceiver scheme.}
  \label{fig:tx_scheme}
\end{figure}

%------------------------------------------------------------------------------
\section{Experimental results}
\label{sec:experimental}

In this sections we consider the experimental results for a generic mesh-based
architecture over a $20mm\times20mm$ die. The ours experiments begin from 
an accurate modelling of a zigzag antenna, selecting the appropriate material and
drawing the structure under test using Ansoft HFSS (High Frequency Structural Simulator), 
a leading commercial finite element method (FEM) field solver which simulate 3D 
structures and produce the main antenna parameters~\cite{hfss}. 
The used set-up is the same seen in~\cite{montusclat_ecwt05} in which considers an high 
resistivity ($\rho=\mathrm{5 K\Omega.cm}$) SOI (Silicon On Insulator) with an substrate's 
thickness of 350 $\mu m$ and  30 $\mu m$ for the oxide ($SiO_2$). The antennas are situated 
at an elevation of 2$\mu m$ from substrate, compatibly with the guidelines reported 
in~\cite{seok_iitc05} for reducing the interference with others metal structure. 
The zigzag antenna have a thickness of 2 $\mu m$ and an axial length of 
$2\times340  \mu m$ for operate around 60 GHz.\\
The main required simulation output are the scattering parameter ($S_{11}$ and $S_{12}$) 
useful for apply the Friis formula an then for calculate the attenuation introduced
by the wireless medium. In particular, the $S_{11}$ allow the determination of antenna's 
bandwidth, reported in the following section.
%------------------------------------------------------------------------------
\subsection{Measured bandwidth and radiation pattern}

In Fig.~\ref{fig:s11} is shown the $S_{11}$ parameter which quantify the portion of
transmitting power that return to power amplifier due to impedance mismatch (50~$\Omega$). 
For a rule of thumbs, we can consider the impedance of antenna matched with the 
transceiver's terminal when at the operating frequency the $S_{11}$ remain under -10 dB. 
We choose this parameter for definite the antenna's band because out of this 
range of frequencies the antenna not only don't work fine as transducer but itself could 
affect the integrity of the power amplifier (PA)  final stage. For this reason, 
seen the results reported in Fig.~\ref{fig:s11}, an bandwidth of about 16 GHz, can provide
a sufficient band for transmitting with a data-rate less of 16 Gbps with an OOK modulation. 
With this informations we can also calculate the antenna's relative bandwidth as:

\begin{equation}
  B_{r}=\frac{B_W}{f_c}=\frac{16 GHz}{60 GHz}\cdot100=0.26
  \label{eq:percentage_band}
\end{equation}
 
where $B_W$ is the previous measured bandwidth while $f_c$ is the resonance frequency. This 
information is useful for determinate at which resonance frequency we should design the antenna 
if we want a data-rate higher than 16 Gbps, or if we want use more bandwidth for a frequency 
division multiplexing (FDM). For example if we want 4 channel with a data-rate of 16 Gbps, we can 
design an antenna with an resonance frequency at least of :

\begin{equation}
  f_c=\frac{B_W}{B_r}=\frac{4\times16 GHz}{0.26}=246 GHz
  \label{eq:op_frequency}
\end{equation}

obtainable scaling properly the dimension of antenna (mainly the axial length).\\
Another important results from simulation is the normalized radiation patter in which we 
can show the antenna's performance when the signal is propagated or received in an specific 
direction (see Sec.~\ref{ssec:friis}). In particular, the dashed black line show the 
directivity at the horizon in which can be observed better performance when the antenna 
transmit or receive in the same direction of their main axis.

\begin{figure}
  \centering
  \includegraphics[width=0.35\textwidth, angle=270]{pictures/radiation.eps}
  \caption{Radiation pattern for zig zag antenna at the horizon (continuous line) and at the 
  elevation of maximum radiations $\phi=35^\circ)$ (dashed line). $\theta=0^\circ$ is the 
  direction parallel to the antennas main axis while $\theta=90$ is the orthogonal direction.}
  \label{fig:radiation}
\end{figure}

\begin{figure}
  \centering
  \includegraphics[width=0.21\textwidth, angle=270]{pictures/s11.eps}
  \caption{$S_{11}$ parameter of the zigzag antenna. The bandwidth is the range of frequency 
  under -10 dB.}
  \label{fig:s11}
\end{figure}
%------------------------------------------------------------------------------
\subsection{Attenuations maps}

After analysing the $s_{11}$ functions and the radiation pattern we has drawn 
the antennas upon the die and we have simulated the worst case $|S_{12}|$ under 
the frequency of interest (the band of frequency considered in the last views 
section) as described in the Sec.~\ref{ssec:pmap_det} for each couple of 
communications. In the experiments we consider a generic WiNoC with 16 radio hub 
or cluster that comprise relative antenna and transceiver upon the considered 
die of ($20mm\times20mm$). For this situation the distance between two antenna 
in the same axis is of 2.5 mm. In Fig.~\ref{fig:pmap} we reported the attenuation 
$G_a$ computed as explained in the Sec.~\ref{ssec:friis} using the 
Eq.~\ref{eq:friis_measured}. Since the antenna exhibit different behaviour when 
is placed a different point of die (as seen in~\cite{gutierez_jsac09}) the measure 
has been conduits consider all the possible position for the transmitting and 
receiving antenna respectively. Fortunately, due to the symmetrical structure 
proper of mesh-based topologies, the measured can be done considering of dividing 
the die in four quarters and placing the transmitter antenna only in one of these. 
In Fig.~\ref{fig:pmap} is shown the attenuation map obtained considering the lower 
left of die. The others attenuation values can evaluated consider that for example 
$G_a(C0,C1)=G_a(C12,C13)=G_a(C15,C14)=G_a(C3,C2)$ and again for reciprocity, 
$G_a(C0,C1)=G_a(C1,C0)$. As just made, we denote with $G_a(Cx,Cy)$ the attenuation 
introduced by the wireless medium for transmit an information from the x to the 
y radio hub.\\
Observing the map in Fig.~\ref{fig:pmap}, we found an important results according 
with the Friis equation seen in the Sec.~\ref{ssec:friis}: the attenuation introduced 
by the wireless medium don't depend only by the relative distance between the radio 
hub but also by the relative orientation. For example if we consider the attenuations 
C0 to C4 and C0 to C3 results: $G_a(C0,C3)<G_a(C0,C4)$ although the distance between 
C0 and C3 is three time much higher respect the distance between C0 to C4. This situation 
is early explained observing the radiation pattern in Fig.~\ref{fig:radiation} in which 
we can see an better performance when the antenna transmit or receive on the proper 
axis direction.

\begin{figure*}
  \centering
  \begin{tabular}{cc}
    \includegraphics[width=0.30\textwidth]{pictures/pmap_c0.eps} &
    \includegraphics[width=0.30\textwidth]{pictures/pmap_c1.eps} \\
    (a) & (b) \\
    \includegraphics[width=0.30\textwidth]{pictures/pmap_c4.eps} &
    \includegraphics[width=0.30\textwidth]{pictures/pmap_c5.eps} \\
    (c) & (d)
  \end{tabular}
  \caption{HFSS Simulation results: attenuation map (Ga) for the clusters C0, C1, C4 and C5.
			The others map can be obtained considering the structure's symmetries.}
  \label{fig:pmap}
\end{figure*}

%------------------------------------------------------------------------------
\subsection{Power saving}
\begin{figure}
  \centering
  \includegraphics[width=0.455\textwidth]{pictures/vga_power.eps}
  \caption{Power Analysis of VGA controller: varying the packet length, 
  the toggle rate of his internal node is reduced.}
  \label{fig:vga_power}
\end{figure}


With the information shown in the previous section, we can compute the power 
at the output of the transmitter under an reliability constrain using the 
Eq.~\ref{eq:pt}. For a BER fixed at $3\times 10^{-14}$ and a data-rate of 16 Gbps, 
we must consider ever an receiver power of -54dBm. This means that the maximum output 
required power is obtained when C0 communicate with C12 (Fig.~\ref{fig:pmap}-a) 
which corresponds an output levels of $P_{t,max}=-54dBm-(-53dBm)=-1 dBm$ that in linear 
scale is equal to $P_{t,max}=794\mu W$. The same calculus can be pursued for an minimum 
required power of -33dBm corresponding at a transmission power of $P_{t,min}=8\mu W$.\\
Finally, considering an adapted versions of the transceiver proposed in~
\cite{daly_jssc07} used also in~\cite{ditommaso_hoti11}, which have 7 adjustable 
output power step, and synthesizing the variable gain controller preciously described 
in RTL using the Synopsys Design Compiler, we can compute the saving obtained  
apply the our proposed scheme to two specific architecture presents in literature
such as McWiNoC~\cite{zhao_nocs11} and iWise~\cite{ditommaso_hoti11}.
For the transceiver we estimate an power consumption of  7mW to 23mW for minimum  
and  maximum required power respectively, corresponding to an energy per bit from  
0.42 pJ/bit to 1.4 pJ/bit.
The powers data for the proposed controller with an control output with 3 bit 
(7 power step), are estimate with an accurate power analysis using Synopsys Power 
Compiler, in which we has created an specific test-bench varying the size of packet. 
The toggle rate of the controller is reduced when the packet length increase because 
it works only when an heater flit is presented at its input (an enable 
input is present, driven by the specific bit presents in the header flit). 
In Fig.~\ref{fig:vga_power}  can be see the power analysis results considering 
an 28nm-CMOS standard cell library from TSMC operating at 1GHz. 
For an packet length of 10 flit we obtain an power consumption 
low as 21 $\mathrm{\mu W}$, negligible respect other components such as transceiver 
and router. The information of this last one has been using DSENT~\cite{Chen_nocs12}.
The due area overhead for the controller is only of 80 $\mathrm{\mu m^2}$ (about 
four order of magnitude respect the a trational transceiver) and his delay is 
about 8 FO4 (fan-out of four).
All the information just exposed have been put all together in a cycle accurate
simulator (a modified version of Noxim~\cite{noxim}) with synthetic traffic,  
for obtain the energy consumption for various experiments in which we have considered 
the following cases:

\begin{enumerate}
	\item	Wire-line: $8\times 8$ concentrated mesh, with 4 IP's for each cluster.
	\item	McWiNoC: The architecture described in~\cite{zhao_nocs11} for a $8\times 8$ 
			mesh with 4 IP's associated each radio hub. This kind of architecture use 
			an TDM multiplexing for the wireless medium. The entire 16 Gbps of bandwidth 
			can be allocate for each communications due to the particular structure of 
			the architecture.
	\item 	Proposed McWiNoC: The precedent case in which we apply the our proposed 
			technique.
	\item 	iWise64: the architecture described in~\cite{ditommaso_hoti11} in which 
			we consider 4 channel with 4 Gbps of bandwidth.
	\item 	Proposed iWise64: the same of the precedent case with the our proposed
			technique.	
\end{enumerate}

\begin{figure}
  \centering
  \includegraphics[width=0.47\textwidth]{pictures/results.eps}
  \caption{Energy consumption for various cases.}
  \label{fig:results}
\end{figure}

The results of each experiments is reported in Fig.~\ref{fig:results} in which we report
the normalized energy (respect the wire-line case). Observing these results, we found
an energy saving of 47.8\%  and 50.2\% when we apply the our proposal to the
architecture at the iWise and McWiNoC cases respectively.
Furthermore, we expect an energy saving about 64.8\% and 60.8\% when the same our
proposed technique are confronted with the wire-based case.



\section{Conclusions and future works}
\label{sec:conclusion}
In this paper the the modulation of transmitter power strength under the reliability 
requirements are for the first time introduced (at the best that we know). After
explained the necessary design step, we have described an specific variable gain controller
in RTL after synthesized at gate-level using Design Compiler, and we have also determinate
the attenuation introduced by the wireless medium with the Friis formula using
HFSS, an accurate 3D field solver. Applying the our technique in the state of 
art mesh-topology based WiNoC architecture we have reduce the power consumption
of the communication infrastructure up to the 50.2\%. A reduction uo to 64.8\% 
respect the wire-based 2d-mesh has been also demonstrated.\\
The introduction of this techniques open new possibility and design challenges
in many direction. The impact of the application mapping can be explored
under the new acquired knowledge. The study of antenna with better relative
bandwidth or with specific radiation pattern (for example that maximize 
the captured power under an possible hotspot directions) should be studied.

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